CSDS seminar – Equidistribution in dynamical systems – Mike Todd

Given an ergodic dynamical system, the proportion of times a typical orbit spends in a given set is asymptotically the measure of that set. We can quantify how close an orbit is to this equidistribution by taking δ > 0 and ε > 0 and seeing how long it takes for the orbit to have hit every δ-ball a proportion of the time greater than (1-ε) times the measure of that ball. Computing the expected value of such a `blanket time is a classical problem in probability, particularly for random walks on finite graphs. Here we give asymptotics for the expectation for small δ, ε, a type of quantitative equidistribution, for a class of dynamical systems. This is joint work with Natalia Jurga.